## Relevant Range

### Learning Outcomes

• Describe the relevant range and its use in managerial accounting

The relevant range is the range of activity where the assumption that cost behavior is a straight line (linear) is reasonably valid. Managerial accountants like to assume that the relationship between a cost and an activity run in a straight line. As an example, if you make 10 widgets, and the direct materials in the widget cost $1, then the assumption would be that for each widget above 10, you would need to purchase another$1 worth of direct materials.

What might make this not be the case? Perhaps, there is a discount on additional direct material at a given point. So from a relevant range standpoint, we need to determine at what point that number will change. Perhaps we get a discount after we purchase 100 components, at which time the cost of direct material will drop to .80 per widget. With variable costs then, the relevant range will be the range where the cost of adding one more, will be the same as the last. In this example, from 0-100 widgets, each additional widget will add $1 in cost to our direct materials. Once we go above 100, we are outside of the relevant range. In fixed expenses, if our facility is designed to build 5,000 widgets per month, what will happen when we reach sales of 5,001 widgets? We will need to add to our space, thus increasing our fixed expenses. ### Example Frank’s Bikes manufacturers children’s bikes. They store the finished inventory in a rented warehouse which is designed to accommodate 25,000 bikes at one time. The warehouse rent per annum is$100,000 regardless of the number of bikes parked there, so it is a fixed cost.

During the financial year 2014, sales dropped but they kept producing bikes so they ended up with too many bikes to store in the rented space. Their ending inventory was 35,000 bikes! They had to rent another space for $50,000 to store the extra finished goods inventory. The new warehouse will be big enough until they reach 55,000 bikes, so the total rent will remain at$150,000 until that time. Hopefully, they get manufacturing and sales aligned before that happens, but for now, that is the new relevant range.

The following graph explains the concept of relevant range. X-axis plots the number of units while Y-axis shows cost.

If they have 25,001 motor bikes in stock, they need the second warehouse! So the relevant range for the cost of $100,000 for rent would be from 0-25,000 bikes. From 25,001 to 55,000 bikes their rent would jump to$150,000. What would happen if they had 55,001 bikes that needed to be stored?

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